Effect of thousands of inelastic couplings on the elastic scattering channel

We describe a new method to solve coupled equations, that arises from the coupled-channel formalism applied to nuclear reactions involving the elastic and inelastic scattering processes. The new technique is faster and presents better numerical convergence than other usual methods. To illustrate the method, in the present paper we have analyzed data for the ⁴He + ²⁰⁸Pb system at E _lab. = 120 and 139 MeV, including thousands of inelastic states with excitation energies up to 80 MeV. However, as a limitation, the method can be used only in the case of couplings connecting directly the inelastic channels to the elastic one, without couplings among the inelastic states. (paper)